Package edu.jas.ufd
Class Quotient<C extends GcdRingElem<C>>
java.lang.Object
edu.jas.ufd.Quotient<C>
- All Implemented Interfaces:
AbelianGroupElem<Quotient<C>>
,Element<Quotient<C>>
,GcdRingElem<Quotient<C>>
,MonoidElem<Quotient<C>>
,QuotPair<GenPolynomial<C>>
,RingElem<Quotient<C>>
,Serializable
,Comparable<Quotient<C>>
public class Quotient<C extends GcdRingElem<C>>
extends Object
implements GcdRingElem<Quotient<C>>, QuotPair<GenPolynomial<C>>
Quotient, that is a rational function, based on GenPolynomial with RingElem
interface. Objects of this class are immutable.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final boolean
final GenPolynomial
<C> Denominator part of the element data structure.private static final org.apache.logging.log4j.Logger
final GenPolynomial
<C> Numerator part of the element data structure.final QuotientRing
<C> Quotient class factory data structure. -
Constructor Summary
ConstructorsModifierConstructorDescriptionQuotient
(QuotientRing<C> r) The constructor creates a Quotient object from a ring factory.Quotient
(QuotientRing<C> r, GenPolynomial<C> n) The constructor creates a Quotient object from a ring factory and a numerator polynomial.Quotient
(QuotientRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d) The constructor creates a Quotient object from a ring factory and a numerator and denominator polynomial.protected
Quotient
(QuotientRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d, boolean isred) The constructor creates a Quotient object from a ring factory and a numerator and denominator polynomial. -
Method Summary
Modifier and TypeMethodDescriptionabs()
Quotient absolute value.int
Quotient comparison.copy()
Clone this.Denominator.Quotient division.Extended greatest common divisor.boolean
Comparison with any other object.factory()
Get the corresponding element factory.Greatest common divisor.int
hashCode()
Hash code for this quotient.inverse()
Quotient inverse.boolean
Is Qoutient a constant.boolean
isONE()
Is Quotient one.boolean
isUnit()
Is Quotient a unit.boolean
isZERO()
Is Quotient zero.monic()
Quotient monic.Quotient multiplication by coefficient.multiply
(GenPolynomial<C> b) Quotient multiplication by GenPolynomial.Quotient multiplication.negate()
Quotient negate.Numerator.Quotient and remainder by division of this by S.Quotient remainder.int
signum()
Quotient signum.Quotient subtraction.Quotient summation.toScript()
Get a scripting compatible string representation.Get a scripting compatible string representation of the factory.toString()
Get the String representation as RingElem.Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Methods inherited from interface edu.jas.structure.MonoidElem
leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
debug
private static final boolean debug -
ring
Quotient class factory data structure. -
num
Numerator part of the element data structure. -
den
Denominator part of the element data structure.
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Constructor Details
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Quotient
The constructor creates a Quotient object from a ring factory.- Parameters:
r
- ring factory.
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Quotient
The constructor creates a Quotient object from a ring factory and a numerator polynomial. The denominator is assumed to be 1.- Parameters:
r
- ring factory.n
- numerator polynomial.
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Quotient
The constructor creates a Quotient object from a ring factory and a numerator and denominator polynomial.- Parameters:
r
- ring factory.n
- numerator polynomial.d
- denominator polynomial.
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Quotient
The constructor creates a Quotient object from a ring factory and a numerator and denominator polynomial.- Parameters:
r
- ring factory.n
- numerator polynomial.d
- denominator polynomial.isred
- true if gcd(n,d) == 1, else false.
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Method Details
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factory
Get the corresponding element factory.- Specified by:
factory
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- factory for this Element.
- See Also:
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numerator
Numerator.- Specified by:
numerator
in interfaceQuotPair<C extends GcdRingElem<C>>
- See Also:
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denominator
Denominator.- Specified by:
denominator
in interfaceQuotPair<C extends GcdRingElem<C>>
- See Also:
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copy
Clone this.- Specified by:
copy
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- Creates and returns a copy of this Element.
- See Also:
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isZERO
public boolean isZERO()Is Quotient zero.- Specified by:
isZERO
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- If this is 0 then true is returned, else false.
- See Also:
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isONE
public boolean isONE()Is Quotient one.- Specified by:
isONE
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- If this is 1 then true is returned, else false.
- See Also:
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isUnit
public boolean isUnit()Is Quotient a unit.- Specified by:
isUnit
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- If this is a unit then true is returned, else false.
- See Also:
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isConstant
public boolean isConstant()Is Qoutient a constant.- Specified by:
isConstant
in interfaceQuotPair<C extends GcdRingElem<C>>
- Returns:
- true, if this has constant numerator and denominator, else false.
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toString
Get the String representation as RingElem. -
toScript
Get a scripting compatible string representation.- Specified by:
toScript
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- script compatible representation for this Element.
- See Also:
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toScriptFactory
Get a scripting compatible string representation of the factory.- Specified by:
toScriptFactory
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- script compatible representation for this ElemFactory.
- See Also:
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compareTo
Quotient comparison.- Specified by:
compareTo
in interfaceComparable<C extends GcdRingElem<C>>
- Specified by:
compareTo
in interfaceElement<C extends GcdRingElem<C>>
- Parameters:
b
- Quotient.- Returns:
- sign(this-b).
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equals
Comparison with any other object. -
hashCode
public int hashCode()Hash code for this quotient. -
abs
Quotient absolute value.- Specified by:
abs
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- the absolute value of this.
- See Also:
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sum
Quotient summation.- Specified by:
sum
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this+S.
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negate
Quotient negate.- Specified by:
negate
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- -this.
- See Also:
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signum
public int signum()Quotient signum.- Specified by:
signum
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- signum(this).
- See Also:
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subtract
Quotient subtraction.- Specified by:
subtract
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this-S.
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divide
Quotient division.- Specified by:
divide
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this/S.
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inverse
Quotient inverse.- Specified by:
inverse
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- S with S = 1/this.
- See Also:
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remainder
Quotient remainder.- Specified by:
remainder
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this - (this/S)*S.
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quotientRemainder
Quotient and remainder by division of this by S.- Specified by:
quotientRemainder
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- a Quotient- Returns:
- [this/S, this - (this/S)*S].
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multiply
Quotient multiplication.- Specified by:
multiply
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this*S.
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multiply
Quotient multiplication by GenPolynomial.- Parameters:
b
- GenPolynomial. - Returns:
- this*b.
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multiply
Quotient multiplication by coefficient.- Parameters:
b
- coefficient.- Returns:
- this*b.
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monic
Quotient monic.- Returns:
- this with monic value part.
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gcd
Greatest common divisor.- Specified by:
gcd
in interfaceRingElem<C extends GcdRingElem<C>>
- Parameters:
b
- other element.- Returns:
- gcd(this,b).
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egcd
Extended greatest common divisor.- Specified by:
egcd
in interfaceRingElem<C extends GcdRingElem<C>>
- Parameters:
b
- other element.- Returns:
- [ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).
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